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- pls provide detailed solution using divergence and p-series find out if the ff. series diverge or converge:Find a power series representing an antiderivative of f(x) = e-(x^4) Use the power series to evaluate lim as x--> 0 of (e-(x^4) + x4 - 1) / x8find a power series that represents the function by modifying the base series for 1/1-x Then, find the interval of convergence of the power series:
- Find taylor series of func f(x)=ln(x) at a=10 (f(x)=sum from 0 to infinity cn(x-10)^n find interval of convergenceA series converges to a sum of 13. The first term has a value of 3. Algebraically determine the exact value of the common ratio.Express the function as the sum of a power series by first using partial fractions. (Give your power series representation centered at x = 0.) f(x) = 2x − 10 x2 − 10x + 9 f(x) = ∞ n = 0 Find the interval of convergence. (Enter your answer using interval notation.)
- Express the function as the sum of a power series by first using partial fractions. f(x) = x + 4 2x2 − 5x − 3 Find the interval of convergence. (Enter your answer using interval notation.)An infinite series is represented by ∑n=1∞(3n415n4+5). What is the limit of the infinite series?Find the taylor series and interval convergence. 7/3-x ln(1-5x)
- How many terms must be taken from the series to calculate the number ln2 using the Taylor Series at the point a=1 of the y=lnx function such that the error is less than 10^-8? Please explain step by stepThe power series in the image converges to cos x for ALL values of x. Using this fact and derivatives, find a power series that converges to sin x. ExplainSuppose sum a(n) x^(n) converges at x=-3 and diverges at x=6. Determine the intervals where the series converges, diverges, or we just don't know. Illustrate please. Image is provided with question. Thanks